MHB Find Integer Solutions for (A+3B)(5B+7C)(9C+11A)=1357911

[anemone]

Find all integer solutions (if any) for the equation $(A+3B)(5B+7C)(9C+11A)=1357911$.

 

[HallsofIvy]

I would start by finding the prime factors of 1375911 (there are five) then forming all groups of 3 factors.

 

[anemone]

Hi HallsofIvy!

Spoiler

Thanks for your reply. But since this is a challenge question, I hope you know our expectation here is to receive a full solution, no more, no less. (Happy)

 

[kaliprasad]

Spoiler: my Solution

No solution because

RHS is odd so all factors are odd so each term in the LHS is odd. there are 3 terms on the LHS and so their sum has to be odd.

but sum is 12A + 8B + 16C which is even so impossible